Mixed regularization for damage mapping in three-dimensional self-sensing composites via EIT

Abstract

Electrical impedance tomography (EIT) is a non-invasive method of spatially mapping the electrical conductivity distribution of a domain based on a limited number of externally collected voltage-current measurements. This modality has been widely explored in the state of the art for damage detection, shaping, and localization in conductive composites (e.g. continuous carbon fiber composites and various nanofiller-modified continuous glass fiber composites) for purposes such as nondestructive evaluation (NDE), structural health monitoring (SHM), and embedded sensing. Mathematically, EIT is an ill-posed inverse problem that requires regularization to solve. To date, materials-focused practitioners of EIT have used relatively simple forms of regularization including, among others, Tikhonov regularization and the discrete Laplace operator (i.e. a smoothness prior). This is limiting because much more advanced types of regularization exist and have potential to significantly improve EIT for material state awareness. Therefore, in this work we propose and experimentally validate a novel mixed form regularization for the EIT inverse problem. In this approach, the discrete Laplace operator or smoothness prior is combined with a conditionally Gaussian prior (i.e. a focal prior). This mixed formulation has the benefit of simultaneously filtering out oscillatory background conductivity perturbations (via the smoothness prior) while still permitting outliers in the solution space (via the focal prior), which is expected to be the case for highly localized damage features in a background of otherwise zero change. The proposed mixed formulation was experimentally validated on two different three-dimensional composites: a carbon black (CB)-modified glass fiber/epoxy tube and a carbon fiber/epoxy laminate shaped as a representative NACA airfoil. Both composite specimens were subject to low-velocity impact damage via a drop-tower rig. It was found that the mixed smoothness + conditionally Gaussian regularization approach markedly outperforms the traditional smoothness only regularization, which allows for much clearer visualization of the damaged state of the material. This work demonstrates the importance of researching advanced regularization methods for materials imaging via EIT.